New Frontiers of Celestial Mechanics: Theory and Applications
I-CELMECH Training School, Milan, Italy, February 3–7, 2020
Page
%P
-
Article
Open AccessExistence proof of librational invariant tori in an averaged model of HD60532 planetary system
We investigate the long-term dynamics of HD60532, an extrasolar system hosting two giant planets orbiting in a 3:1 mean motion resonance. We consider an average approximation at order one in the masses which r...
-
Book and Conference Proceedings
-
Chapter and Conference Paper
Invariant KAM Tori: From Theory to Applications to Exoplanetary Systems
We consider the classical problem of the construction of invariant tori exploiting suitable Hamiltonian normal forms. This kind of approach can be translated by means of the Lie series method into explicit com...
-
Article
Exponential Stability in the Perturbed Central Force Problem
We consider the spatial central force problem with a real analytic potential. We prove that for all analytic potentials, but for the Keplerian and the harmonic ones, the Hamiltonian fulfills a nondegeneracy pr...
-
Article
A reverse KAM method to estimate unknown mutual inclinations in exoplanetary systems
The inclinations of exoplanets detected via radial velocity method are essentially unknown. We aim to provide estimations of the ranges of mutual inclinations that are compatible with the long-term stability o...
-
Article
Rigorous estimates for the relegation algorithm
We revisit the relegation algorithm by Deprit et al. (Celest. Mech. Dyn. Astron. 79:157–182, 2001) in the light of the rigorous Nekhoroshev’s like theory. This relatively recent algorithm is nowadays widely used ...
-
Article
Secular dynamics of a planar model of the Sun-Jupiter-Saturn-Uranus system; effective stability in the light of Kolmogorov and Nekhoroshev theories
We investigate the long-time stability of the Sun-Jupiter-Saturn-Uranus system by considering a planar secular model, which can be regarded as a major refinement of the approach first introduced by Lagrange. I...
-
Article
Improved convergence estimates for the Schröder–Siegel problem
We reconsider the Schröder–Siegel problem of conjugating an analytic map in \(\mathbb {C}\) ...
-
Article
On the convergence of an algorithm constructing the normal form for elliptic lower dimensional tori in planetary systems
We give a constructive proof of the existence of elliptic lower dimensional tori in nearly integrable Hamiltonian systems. In particular we adapt the classical Kolmogorov normalization algorithm to the case of...
-
Article
Effective stability around the Cassini state in the spin-orbit problem
We investigate the long-time stability in the neighborhood of the Cassini state in the conservative spin-orbit problem. Starting with an expansion of the Hamiltonian in the canonical Andoyer-Delaunay variables...
-
Article
On the extension of the Laplace-Lagrange secular theory to order two in the masses for extrasolar systems
We study the secular evolution of several exoplanetary systems by extending the Laplace-Lagrange theory to order two in the masses. Using an expansion of the Hamiltonian in the Poincaré canonical variables, we...
-
Article
A semi-analytic algorithm for constructing lower dimensional elliptic tori in planetary systems
We adapt the Kolmogorov’s normalization algorithm (which is the key element of the original proof scheme of the KAM theorem) to the construction of a suitable normal form related to an invariant elliptic torus...
-
Article
Kolmogorov and Nekhoroshev theory for the problem of three bodies
We investigate the long time stability in Nekhoroshev’s sense for the Sun– Jupiter–Saturn problem in the framework of the problem of three bodies. Using computer algebra in order to perform huge perturbation e...
